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Vex2-byte1

!vex2-byte1->vvvv

Update the |X86ISA|::|VVVV| field of a vex2-byte1 bit structure.

Signature
(!vex2-byte1->vvvv vvvv x) → new-x
Arguments: vvvv — Guard (4bits-p vvvv).; x — Guard (vex2-byte1-p x).
Returns: new-x — Type (vex2-byte1-p new-x).

Definitions and Theorems

Function: !vex2-byte1->vvvv$inline

(defun !vex2-byte1->vvvv$inline (vvvv x)
  (declare (xargs :guard (and (4bits-p vvvv) (vex2-byte1-p x))))
  (mbe :logic
       (b* ((vvvv (mbe :logic (4bits-fix vvvv)
                       :exec vvvv))
            (x (vex2-byte1-fix x)))
         (part-install vvvv x :width 4 :low 3))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 8) -121)))
                          (the (unsigned-byte 7)
                               (ash (the (unsigned-byte 4) vvvv)
                                    3))))))

Theorem: vex2-byte1-p-of-!vex2-byte1->vvvv

(defthm vex2-byte1-p-of-!vex2-byte1->vvvv
  (b* ((new-x (!vex2-byte1->vvvv$inline vvvv x)))
    (vex2-byte1-p new-x))
  :rule-classes :rewrite)

Theorem: !vex2-byte1->vvvv$inline-of-4bits-fix-vvvv

(defthm !vex2-byte1->vvvv$inline-of-4bits-fix-vvvv
  (equal (!vex2-byte1->vvvv$inline (4bits-fix vvvv)
                                   x)
         (!vex2-byte1->vvvv$inline vvvv x)))

Theorem: !vex2-byte1->vvvv$inline-4bits-equiv-congruence-on-vvvv

(defthm !vex2-byte1->vvvv$inline-4bits-equiv-congruence-on-vvvv
  (implies (4bits-equiv vvvv vvvv-equiv)
           (equal (!vex2-byte1->vvvv$inline vvvv x)
                  (!vex2-byte1->vvvv$inline vvvv-equiv x)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->vvvv$inline-of-vex2-byte1-fix-x

(defthm !vex2-byte1->vvvv$inline-of-vex2-byte1-fix-x
  (equal (!vex2-byte1->vvvv$inline vvvv (vex2-byte1-fix x))
         (!vex2-byte1->vvvv$inline vvvv x)))

Theorem: !vex2-byte1->vvvv$inline-vex2-byte1-equiv-congruence-on-x

(defthm !vex2-byte1->vvvv$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (!vex2-byte1->vvvv$inline vvvv x)
                  (!vex2-byte1->vvvv$inline vvvv x-equiv)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->vvvv-is-vex2-byte1

(defthm !vex2-byte1->vvvv-is-vex2-byte1
  (equal (!vex2-byte1->vvvv vvvv x)
         (change-vex2-byte1 x :vvvv vvvv)))

Theorem: vex2-byte1->vvvv-of-!vex2-byte1->vvvv

(defthm vex2-byte1->vvvv-of-!vex2-byte1->vvvv
  (b* ((?new-x (!vex2-byte1->vvvv$inline vvvv x)))
    (equal (vex2-byte1->vvvv new-x)
           (4bits-fix vvvv))))

Theorem: !vex2-byte1->vvvv-equiv-under-mask

(defthm !vex2-byte1->vvvv-equiv-under-mask
  (b* ((?new-x (!vex2-byte1->vvvv$inline vvvv x)))
    (vex2-byte1-equiv-under-mask new-x x -121)))